Class 12 Physics Formulas

Complete List of All Class 12 Physics Formulas: Chapter-wise PDF Download

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After Class 10, for students who choose science irrespective of medical or non-medical field, Class 12 Physics is an integral part and somehow becomes a difficult subject to understand. Slowly students, after seeing complex numerical problems, need more understanding and many even start failing the subject.

To understand the concepts, Class 12 Physics Formulas play a significant role not only in the CBSE 2024 board exams but in the further competitive exams as well. The formulas can help students solve the problem directly and in a structured manner. This will also help in clearing the fundamentals of the chapters.

At Educart, the Class 12 Physics formulas list is provided based on NCERT and the latest CBSE pattern to help students find the formula list in one place and be able to score their dream marks.

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General Physics Formulas for Class 12

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1. Faraday constant F = 96485 C/mol
2. Bohr magneton µ_B = 9.27 × 10⁻²⁴ J/T 
3. Planck constant h = 6.63 × 10⁻³⁴ J.s = 4.136 × 10^-15 eV.s
4. Wien displacement constant b = 2.9 × 10⁻³ m K
5. Rydberg constant R_∞ = 1.097 × 10⁷ m⁻¹
6. Molar gas constant R = 8.314 J/(mol K)
7. Mass of proton m_p = 1.6726 × 10⁻²⁷ kg
8. Mass of electron m_e = 9.1 × 10⁻³¹ kg
9. Coulomb constant 1/4πε₀ = 8.9875517923(14) × 10⁹ N m²/C²
10. Gravitation constant G = 6.67×10⁻¹¹ m³ kg⁻¹ s⁻²
11. Mass of neutron m_n = 1.6749 × 10⁻²⁷ kg
12. Permittivity of vacuum 0 = 8.85 × 10⁻¹² F/m
13. Charge of electron e = 1.602 × 10⁻¹⁹ C

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Class 12 Physics All Formulas Chapter Wise

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The Class 12 Physics formulas will help in exam preparation in fast calculations. The formula PDF has it all from simple formulas to the most difficult formulas. The section below has chapter-wise formula links and important topics. 

Chapter 1: Electric Charges and Fields

Physics Chapter 1 Electric Charges and Fields covers all the important topics like Basic Introduction, Conservation of charge, superposition principle, electric field, Coulomb’s law, electric flux, Gauss Theorem, and its applications. 

Electric Charge

Properties of Charges

• Quantisation of Charge

q = ± ne

Where n is the number of electrons transferred and e^– is the basic electron charge.

• Additive Property of Charges

q_net = Σq_i

Where, i = 1, 2, 3. . . . n.

• Conservation of Charge/ Law of conservation of charge

→ The total charge of an isolated system remains constant.

→ The electric charges can neither be created nor be destroyed, but can only be transferred from one body to another.

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Coulomb force between two point charges

Here e₀ is known as the permittivity constant of free space and has a value of 8.85 × 10^–12 C²N^–1m^–2. The S.I. unit of force is Newton (N).

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1 Coulomb

1C is the charge which when placed 1 m away from another 1C charge exerts a force of 9 × 10⁹N on each other.

As per Newton's third law, 

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Superposition of Forces

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Electric Field and Electric Dipole

Electric Field

Here, Q is known as the source charge, and q is known as the test charge. If the test charge is of 1 C then numerically the field is equal to the force of the source charge on the test charge. Hence, the force can be defined as

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Superposition of Fields

If multiple charges are around a certain point then the net electric field at a given point is the vector sum of all fields. It is given by,

Electric Field Lines and Properties

Electric Field Lines

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Representation of Electric Fields

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Field Near a Conductor

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Field between two charged conductors Continuous Charge Distributions

Electric Dipole

Dipole Moment of the Dipole

The dipole moment of the dipole is given by, p = q (2a)

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Field on the axis

• For a large distance where r >> a

• In terms of dipole moment, it translates into;

Field on the equator

• For a large distance where r >> a

• In terms of dipole moment, it translates into;

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Dipole in a Uniform Electric Field

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Electric Flux and Gauss's Theorem

Continuous Charge Distribution

• Area charge density or surface charge density

• Volume Charge Density

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Electric Flux

 ΦE stands for Electric flux

Unit of  ΦE = unit of E × unit of S

∴ SI unit of Electric Flux = Nm² C^-1 or Vm^-1 m² = Vm

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Gauss's Theorem

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Application of Gauss's Theorem

• Field due to infinitely long charged wire

• Field due to an infinite plane lamina

• Field due to a uniformly charged spherical shell

On the surface and outside the shell

Inside the shell

Chapter 2: Electrostatic Potential and Capacitance

Physics Chapter 2 Electrostatic Potential and Capacitance covers all the important topics like Electric charges, electric potential due to a point charge, and capacitance of a parallel plate capacitor with and without dielectric medium between the plates. 

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Electrostatic Potential

Potential Due to a Charge

Amount of Work Being Done in Moving The Test Charge

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Potential Energy

ΔU = U_P – U_R

= W_RP

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Electric Potential

U = U_P – U_∞

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Electrostatic Potential

Potential Due to a Point Charge

Electrostatic Potential of a charge Q at a distance r

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Variation of Electric Field and Potential Due to a Point Charge

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Potential Due to a Dipole

Dipole Moment

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Electrostatic Potential

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On the axis of a dipole

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Equipotential Surfaces

Various Equipotential Surfaces

Relation between field and potential

Potential Energy of a System of Charges

Multiple Charge Configuration

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The Potential Energy of the System

Potential Energy in an External Field

Potential Due to a System of Charges

Potential Due to Multiple Charges

Potential at any point P is given as

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Dipole

Electrostatics of Conductors

 Distinguish Between Conductors, Insulators, and Dielectrics

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Constant Potential Inside

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Electrostatic Shielding

Polarization

P = e_{0 ce}E

Chapter 3: Current Electricity

Electric Current

Ohm’s Law

Below, ρ denotes the resistivity of the material.

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Current Density

⇒ 

⇒

j = σE

Where σ denotes conductivity which is the reverse of resistivity.

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Variation of V Vs I

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Drift Speed

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Origin of Resistivity of Any Material

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Mobility

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Temperature Dependence of Resistivity

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Electrical Energy and Power

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Cells, EMF, and Internal Resistance

Cells in Series

E = E₁ + E₂

And r = r₁ + r₂ 

The net EMF is the sum of both EMFs and net resistance is the sum of internal resistances.

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Cells in Parallel

Kirchhoff’s Rules

Junction Rule

ΣI = 0

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Loop Rule

Σ (E-Ir) = 0

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Wheatstone Bridge

Chapter 4: Moving Charges and Magnetism

Physics Chapter 4 Moving Charges and Magnetism covers all the important topics like Oersted's experiment, biot-savart law, ampere’s law, moving coil galvanometer, and force on a moving charge in uniform magnetic and electric fields. 

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Motion and Force in a Magnetic Field

Magnetic Field and Lorentz Force

Where, E = Electric field, B = Magnetic Field. This force is known as the Lorentz Force.

• The unit of the magnetic field is Tesla.
• 1 Gauss = 10^–4 Tesla

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Magnetic Force on a Current-Carrying Conductor

Where j = current density

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Motion in a Magnetic Field

The pitch of the Helix.

Pitch = v_y T

Where, v_y = v_||

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Magnetic Field Due to a Current Element

Biot-Savart Law

Which can also be written as

Where

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Magnetic Field on the Axis of a Circular Current Carrying Loop

The field at P due to the current element is given by,

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This leads us to two cases

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Ampere’s Circuital Law

∫ B.dl = μ_oI

Then, Magnetic Field

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Solenoid

Chapter 5: Magnetism and Matter

Physics Chapter 5 Magnetism and Matter covers all the important topics like bar magnet as an equivalent solenoid, magnetic field intensity due to a magnetic dipole (bar magnet), para-, dia-, and ferromagnetic substances, and the effect of temperature on magnetic properties. 

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The Bar Magnet and Magnetic Dipole

Field lines of a Bar Magnet

• Magnetic moment m and electric dipole moment p.

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Electrostatic Analog

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Gauss’s Law of Magnetism

Imagine a small area vector dS such that the flux through it can be stated as

ΦB = ∫B . dS

Unlike electrostatics in magnetism, the flux is zero.

ΦB = 0

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Magnetic Properties of Materials

Magnetization

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Magnetic Intensity

M = χH

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Magnetic Susceptibility

B = μ0 (1 + χ ) H = μ0μr H = μH

Where μr = 1 + χ is known as relative permeability.

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Susceptibility of Various Types of Materials

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Curie’s Law

Chapter 6:  Electromagnetic Induction 

Physics Chapter 6 Electromagnetic Induction covers all the important topics like Faraday's law, induced EMF, and current, Lenz’s law, self, and mutual induction. 

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The Basics of Electromagnetism

Magnetic Flux

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The total magnetic field passing through an area of cross-section

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Dimensions of magnetic flux

SI Unit of Magnetic flux

1 Wb = 1 Tm²

Relation Between Weber and Maxwell

1 Wb = 1 Tm² = 10⁴ × 10⁴ cm²

1 Weber = 10⁸ maxwell

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Faraday’s Laws

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Lenz’s Law

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Motional EMF

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Inductance

M₂₁ = μ_on₁n₂πr₁² l

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Self Inductance

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AC Generator

E = E_o sin2πνt

Where, ω = 2πv, E_o = NBAω

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Chapter 7: Alternative Current

Alternating Current and Ac Circuits

Kirchhoff's Loop Rule

Instantaneous EMF of the source = Instantaneous potential difference across R.

I_m is known as current amplitude.

The sum of instantaneous current values over one complete cycle is zero and the average current is zero.

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Phasor Diagram

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AC Voltage Applied to an Inductor

This circuit is purely inductive A.C. circuit.

It is the peak value of A.C.

ωL is known as Inductive Reactance, denoted by XL. SI unit is ohm (Ω).

X_L = ωL

The instantaneous power supplied to an inductor is,

So, the average power of the complete cycle is

The average power supplied to an inductor over one complete cycle is zero.

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AC Voltage Applied to a Capacitor

The voltage across the capacitor is given by,

Where the amplitude of oscillating current is, I_m = ωCV_m

The instantaneous power supplied to the capacitor is,

And the average power of the complete cycle is given by,

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LCR Circuit and AC Devices

AC Through L-C-R

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Phasor-diagram Solution

I = I_m sin (ωt + φ)

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Phase Angle

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Resonance

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Resonating Frequency

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The Power Factor

= VI cos φ

It can also be written as, P = I² Z cos φ

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Transformer

• In a step-up transformer, N_p > N_s, the turn ratio is greater than 1, hence output voltage is greater than the input voltage.
• In a step-down transformer, N_s > N_p, the turn ratio is less than 1, hence output voltage is less than input voltage.
• Real transformers are 90-99% efficient. Small energy losses occur in real transformers due to flux leakage, resistance of the windings, eddy currents, or hysteresis.

Chapter 8: Electromagnetic Waves

Physics Chapter 8 Electromagnetic waves cover all the important topics like areas under simple curves. 

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Displacement Current and Electromagnetic Waves

Ampere’s Circuital Law

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Ampere-Maxwell Law

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The Relation Between Magnetic Field and Electric Field is Given By,

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Electromagnetic Spectrum in Increasing Order of Frequency and Decreasing Order of Wavelength

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Chapter 9: Ray Optics and Optical

Physics Chapter 9 Ray Optics and Optical covers all the important topics like total internal reflection, linear magnification, power of the lens, and refraction through a prism, microscope, and telescope. 

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Reflection of Light by Spherical Mirrors

Focal Length of Spherical Mirrors

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Here, C is the center of curvature, and F is the Principal Focus of the mirror.

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The Mirror Equation

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Linear Magnification

• When m > 1, an image formed is enlarged.
• When m < 1, an image formed is diminished.
• When m is positive, the image must be erect, i.e., virtual.
• When m is negative, the image must be inverted, i.e., real.

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Refraction

Snell’s Law

The refractive index μ of a material is the ratio of the speed of light (c) in vacuum to the speed of light in the medium (v).

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Total Internal Reflection

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Refraction by Lenses

Magnification by the lens is the ratio of the image to that of the object.

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Power Of A Lens

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Lens Formula

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Power of Lenses

P = P₁ + P₂ + P₃ +.........+ P_n

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Prism and Optical Instruments

Refraction Through a Prism

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Total Deviation

δ = i + e – A

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Refractive Index of Prism

Minimum deviation Dm,

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Simple Microscope

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Total magnification

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Compound Microscope

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Total magnification

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Telescope

Chapter 10: Wave Optics

Physics Chapter 10 Wave Optics covers all the important topics like Huygens principle, Interference of light, polarisation, and many more.

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Refraction of Plane Wave

If c represents the speed of light, then

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Snell’s law of refraction

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Refraction at a Rarer Medium

n₁sin i = n₂ sin r

i_c = n₂/n₁

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Reflection of Plane Wave by a Plane Surface

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The Doppler Effect

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Condition For Constructive Interference

Resultant Intensity at a Point Is Maximum When

cos φ = 1 or φ = 0, 2 p, 4p

path difference is p = 0, λ, 2λ ….. = nλ

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Condition For Destructive Interference

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Young’s Double Slit Experiment

Path difference, p = S₂P – S₁P

Position of bright fringes, for consecutive interference

For central bright fringe n = 0,

For n^th bright fringe: 

Position of dark fringe, for destructive interference

For the first dark fringe n = 1,

For n^th dark fringe

Width of a dark fringe = separation between two consecutive bright fringes

Intensity is proportional to the square of amplitude.

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The Single Slit

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• Calculation of path difference 

P = BP – AP = d sin q

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• Position of minima 

d sin θ₁ = λ

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• n^th dark fringe

d sin q_n = nλ, n = 1, 2, 3…

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• Position of the n^th secondary maximum

Chapter 11: Dual Nature of Radiation and Matter

Physics Chapter 11 Dual Nature of Radiation Matter covers all the important topics like electron emission and reflection, photoelectric effect, and many more.

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Electron Emission and Photoelectric Effect

One electron volt (eV)

1 eV = 1.602 × 10^–19 J

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Work Functions of Some Metals

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Effect of Intensity of Light on Photoelectric Current

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Effect of Potential on Photoelectric Current

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Stopping Potential

K_max = eV_o

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Effect of Frequency of Incident Radiation on Stopping Potential

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Einstein's Photoelectric Equation

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Broglie wavelength

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Chapter 12: Atoms

Physics Chapter 12 Atoms covers all the important topics like Bohr’s model and line spectra of the hydrogen atom, the trajectory of α particles, electron orbits, de-broglie’s explanation, and atomic spectra.

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Physics of the Atom

Alpha-Particle Scattering and Rutherford's Nuclear Model of Atom

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Observations in Rutherford's Nuclear Model of Atom

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Magnitude of this force

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Alpha - Particle Trajectory

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Electron Orbit

• the radius of the orbit and electron velocity

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• The kinetic energy (K) and electrostatic potential energy (U) of the hydrogen atom

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• Total Electron Energy

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Bohr's Model of the Hydrogen Atom

Angular Momentum (L) of the Orbiting Electron is Quantized

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Frequency of the Emitted Photon

h_ν = E_i – E_f

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Bohr’s second postulate

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Relation between v_n and r_n

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The total energy of the electron

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The Line Spectra of Hydrogen Atom

Rydberg Formula

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Balmer series

Chapter 13: Nuclei

Physics Chapter 13 Nuclei covers all the important topics like basic terms and concepts, nuclear binding energy, radioactivity, and radioactive decay.

Atomic Mass and Composition Of Nucleus

• 1 amu = ¹/₁₂ × Mass of the carbon 12-atom
• 1 amu = ¹/₁₂ × 1.992678 × 10^–26 kg
• 1 amu = 1.660565 × 10^–27 kg
• Z = No. of protons in an atom = No. of an electron in an atom = Atomic Number
• N = No. of neutrons in an atom = Neutron number
• A = No. of nucleons in an atom = Mass number = (Z + N) = Total no. of proton and neutron. where Z = Atomic No; A = Mass No; X = Chemical symbol of the element
• Symbolically Representation

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Size Of Nucleus

• The volume of the nucleus is directly proportional to its mass number.

• Density formula

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Mass - Energy and Nuclear Binding Energy

Mass-Energy 

E = mc²

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Nuclear Binding Energy

ΔE_b = Δm × c²

Δm = [Zm_p + (A – Z) m_n]^–M

Binding energy per nucleon is the average energy to extract a single nucleon from the nucleus.

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Nuclear Force

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Nuclear Energy

Fission

Let, A = 240 breaks into A₁ and A₂ of 120

E_bn for A = 7.6 MeV

E_bn for A₁ and A₂ = 8.5 MeV

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Chapter 14: Semiconductor Electronics: Materials, Devices, and Simple Devices

Physics Chapter 14 Semiconductor Electronics covers all the important topics like classification based on conductivity, intrinsic, and extrinsic metal, and many more.

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Classification of Metals, Conductors, and Semiconductors

Classification based on Conductivity

• Metals: High conductivity,

σ = 10² to 10⁸ Sm^–1

• Semiconductors: Intermediate conductivity,

σ = 10⁵ to 10^–6 Sm^–1

• Insulators: Low conductivity,

σ = 10^–11 to 10^–19 Sm^–1

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Classification based on Energy Bands

E_g = 1.17 eV for Si

E_g = 0.74 eV for Ge

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Intrinsic Semiconductors

• n_i = n_e = n_h

Intrinsic carrier concentration = number of free electrons = number of holes.

• total current is,

I = I_c + I_h; where I_c is electron current under an applied electric force and I_h is hole current

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Extrinsic Semiconductors

• n-Type Semiconductors; n_e >> n_h

• p-Type Semiconductors; n_h >> n_e

• The electron and hole concentration in a semiconductor in thermal equilibrium is given by,  n_e. n_h = n_i²

Applications of Class 12 Physics Formula

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The Class 12 Physics formulas aren’t only applicable from the exam’s perspective but it is used in many fields in the real world like scientific research and technology. It will be helpful for every student who especially wants to pursue a career in science research and technology fields. Below are some of the many real-life applications of the Class 12 Physics formulas.

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• Fluid mechanics is highly used in the aeronautics department for designing and structuring aircraft. It is also highly useful in trying to understand how many fluids and air behave in motion.
• The medical and clinical instruments along with communication tools use the phenomena of laser stimulation emission.
• Our day-to-day household appliances use the basics of Ohm’s law for designing purposes.
• For the optimization of heat engines and their design, the Carnot efficiency formula in physics is used. 

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In Physics class 12 all formulas have lots of real-life applications like in nuclear plants, transistors and semiconductors in daily appliances and many more help us in our day-to-day life.

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How to Prepare for the CBSE 2024 Physics Board Exams?

Since CBSE has already notified students regarding the announcement of board exams on January 15, 2024, the preparation must have been started. Although many students still might be wondering how to start preparing for the CBSE 2024 physics board exams, a few tips and tricks might help in getting a kickstart.

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• Understand the Class 12 CBSE Physics Syllabus. You may find it at the official site or can download it from here.
• Refer to Class 12 NCERT books and reference books like Concepts of Physics by H.C Verma along with Youtube one-shots to understand the concept. Make sure to make revision notes simultaneously. 
• Practice NCERT in-text and exercise questions and use the above-mentioned formulas to solve them quickly.
• Practice the latest pattern questions since CBSE has introduced 50% of questions in the board exams, you can also use additional practice papers introduced by CBSE.
• Attempt Sample Paper Questions from Educart Class 12 Physics Sample Paper book as it covers CBSE-pattern, competency-based questions, PYQs, and follows the latest syllabus.
• Make sure you practice regularly and clear your doubts timely.

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You can use memorization techniques like mind maps, Feynman Technique, Colourful memory notes, and many more to study smartly.  The formulas PDFs for Class 12 Physics comprise all the major formulas in the Class 12 CBSE syllabus. Prepare well and practice regularly.